Question

5. Determine k so that k +2.4k - 6 and 3k - 2 are the three consecutive terms of an A.P.​

Answer 1

Answer :

k = 3

Step-by-step explanation :

Given,

• k + 2, 4k - 6 and 3k - 2 are the three consecutive terms of an A.P.​

To find,

• the value of k

Solution,

Since,

Arithmetic Progression is the sequence of numbers such that the difference between any two successive numbers is constant.

   4k - 6 - (k + 2) = 3k - 2 - (4k - 6)

   4k - 6 - k - 2 = 3k - 2 - 4k + 6

   3k - 8 = -k + 4

   3k + k = 4 + 8

      4k = 12

        k = 12/4

        k = 3

The value of k is 3

Verification :

Substitute k = 3,

⟿ k + 2 = 3 + 2 = 5

⟿ 4k - 6 = 4(3) - 6 = 12 - 6 = 6

⟿ 3k - 2 = 3(3) - 2 = 9 - 2 = 7

The consecutive terms are 5 , 6 , 7

➝    6 - 5 = 1

➝    7 - 6 = 1

The difference is same

Hence they're in A.P

Answer 2

Answer:

(k+2)+(3k−2)=2(4k−6)

⇒4k=8k−12

⇒4k−8k=−12

⇒−4k=−12

⇒4k=12

⇒k=

4

12

=3

Hence k=3.